This invention relates to the nonuniform translation of analog signals and digital signals, one to the other, using piece-wise linear processes to approximate a modified logarithmic response characteristic in the coder and decoder. The nonuniform translation in particular yields a companding effect during the conversion process with volume compression or expansion as appropriate.
The translation processes disclosed in this invention relate to digital transmission, and in particular transmission by PCM (Pulse Code Modulation). The advantages of PCM over other forms of modulation are well known in the art. See, for example, the article "Philosophy of PCM," by Oliver, Pierce, and Shannon, in volume 36, Proceedings of the I.R.E., pages 1324-1331 (1948). The distinct advantage of the transmission of information by PCM is that the information is digital in nature and may therefore be regenerated by repeaters employed along the transmission path. The regeneration process substantially eliminates the accumulation, in the course of transmission, of noise, crosstalk, and other forms of signal degradation.
Prior to transmission, coding (i.e., conversion of the original analog information to a pulse code) is necessary in a PCM system; and if the digital information thus transmitted is to be used in its original form upon its reception, decoding is necessary.
During encoding of the original information it is necessary that the coder output be quantized. In the quantizing process the exact value of the information at any instant is approximated by one of a number of discrete codes. Information is thus represented by a discrete number of quantum levels. The difference between the instantaneous value of the original information and the quantum level actually transmitted is known as quantizing error and gives rise to what is called either quantizing noise or quantizing distortion. If the quantum levels are chosen in regular intervals through the signal amplitude range, it is apparent that the percentage error will not be constant for samples of all sizes. In this case, the large signals can tolerate rather large quantizing noise figures while maintaining a reasonable percentage of error, while smaller signals yield a greater percentage of error for comparable quantizing noise levels. Thus, it is desirable to keep the signal-to-quantizing noise ratio at a fairly constant value over the signal amplitude range. In order to maintain a constant value, it is necessary to have more quantum levels available at low signal amplitudes. In this way, the low signal amplitudes are more accurately defined, thereby reducing the quantizing error.
One technique that is used, in the reduction of quantizing noise, is volume compression and volume expansion, which is well-known, to those skilled in the art, as companding. In companding, the number of quantizing levels in the small signal range are more numerous than in the larger amplitude ranges; that is, they are compressed in the smaller signal range. The express purpose of companding is the maximization of the ratio of average signal-to-quantizing noise over the amplitude range. In this manner, quantizing noise is rather evenly distributed on a percentage basis, and is relatively minimized. It is noteworthy that companding is an inherently nonlinear process, with the prevalent companding functions being either logarithmic or hyperbolic functions.
Companding requirements are different for signals having different characteristics. In order to obtain an acceptable level of quantizing noise, voice signals require constant signal-to-distortion ratios over a wide dynamic range. In particular, additional quantizing steps are required for the low signal amplitudes. The quantizing distortion should be proportional to signal amplitude for any signal level, which means that for voice signals a logarithmic compression law should be used. For a discussion of the logarithmic compression law and practical methods for modifying same, reference may be made to the wealth of publications on this subject. In particular the now well-known .mu.-law modification of the logarithmic function is discussed in detail in an article by B. Smith, "Instantaneous Companding of Quantized Signals," Bell System Technical Journal, vol. 36, May 1957, pp. 653-709. An expression for the .mu.-law characteristic over a normalized coding range of .+-.1 is: ##EQU1## Where x is small, the F(x) approaches a linear function, and for a large x it approaches a logarithmic function. The range of signal power over which the signal-to-distortion ratio is relatively constant is determined by the parameter .mu.. For a relatively constant signal-to-distortion ratio over a 40-dB dynamic range .mu. should be greater than 100.
A second method of approximating the true logarithmic law is described by K. W. Cattermole, in a discussion on a paper by R. F. Purton, Proc. IEE, vol. 109, Part B, pp. 485-487, in which a true logarithmic curve is smoothly joined to a linear segment at low levels. The expressions for this A-law characteristic is given by the following expressions: ##EQU2## The two logarithmic laws can be approximated by nonlinear devices such as diodes, and these laws can also be implemented by a piece-wise linear approximation using several segments.
The digitally linearizable laws are an interesting class of piece-wise linear compression laws. These laws are characterized by the property that the coding intervals, which are equal within each segment, are integral multiples of the size of a smallest coding interval.
Of particular interst for binary word coders are the cases where the coding intervals are related by powers of two, and each linear segment contains an equal number of coding intervals. The A-law and .mu.-law characteristics described above are of this type. For a more detailed discussion see E. J. Anderson, "Considerations in Selection of a M.mu. = 255 Companding Characteristic," 1970 International Conference of Communications, vol. 19, pp. 7-9-7-19. For example, 8 segments on each side of 0 are commonly used. If the size of the coding intervals with each segment doubles for each segment outward from the center, a 15-segment digitally linearizable law results, which approximates the .mu.-law characteristic with .mu. = 255. The ratio of the largest to smallest coding interval (the compression factor) is 2.sup.7 = 128; the compandor improvement for small signals is 30 dB. If the center 4 segments of the 8 original segments on each side of 0 are made co-linear, with the coding intervals of the remaining outer segments doubling in size as before, a 13-segment digitally linearizable compression law is achieved. This compression law approximates the A-law characteristic, matching the slope at the origin with A = 87.6. The compression factor is 2.sup.6 = 64; the companding improvement for a small signal is 24 dB.
Traditionally, practical PCM systems have featured separate compression and linear encoding units at their transmitting end as well as separate linear decoding and expanding units at the receiving ends. Within the past few years, PCM systems have been developed in which the companding and coding functions have been combined. Typical of the techniques used in combining of the coding and companding functions is illustrated by the system disclosed by R. L. Carbray in U.S. Pat. No. 2,889,409. Exemplary of the Carbray invention is the transmitting end of the system in which a nonlinear encoder automatically compresses its input signal as it carries out its coding operation. B. D. Smith discloses a method of nonlinear encoding by feedback methods in an article entitled, "Coding by Feedback Methods," which appears in volume 41 of the Proceedings of the I.R.E. at page 1053. Another such technique is disclosed by Bonami et al in U.S. Pat. No. 3,653,033.
While the method of conversion between analog and digital information which has been disclosed by Carbray, Smith, and Bonami et al. has many advantages, the objects attained by the presently disclosed invention and the features and advantages thereof constitute an important contribution to the field of the PCM communication.
It is a principal object of this invention to use the characteristics of nonuniform coding and decoding such that the implementation is achieved in a simple and straightforward and inexpensive manner. Another object of the invention is that high accuracies are not required for any of the circuit components.
Still another object of the invention is to readily maintain the monotonicity at the intercepts of the signals for the piece-wise linear approximation of the companding characteristic. Further, the co-linearity of the two segments about zero is maintained. This latter results in a near perfect symmetry in the coder response for both positive and negative signals.